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Science
Author: Rudy Rucker
ISBN: 0691001723
Subcategory: Mathematics
Pages 352 pages
Publisher Princeton University Press; New edition edition (May 15, 1995)
Language English
Category: Science
Rating: 4.9
Votes: 930
ePUB size: 1753 kb
FB2 size: 1770 kb
DJVU size: 1274 kb
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eBook Infinity and the Mind download

by Rudy Rucker


Rudy Rucker's Infinity and the Mind is a terrific study with real mathematical depth. Rudy Rucker, set theorist and science-fiction author, has continued the tradition.

Rudy Rucker's Infinity and the Mind is a terrific study with real mathematical depth. Infinity and the Mind is funny, provocative, entertaining, and profound. --Joseph Shipman, Journal of Symbolic Logic. Attempts to put Gödel's theorems into sharper focus, or at least to explain them to the nonspecialist, abound.

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical.

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic.

These include Godel's incompleteness theorems and their.

These include Godel's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane.

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane

A mathematician with philosophical interests, Rucker published Infinity and the Mind in 1982.

A mathematician with philosophical interests, Rucker published Infinity and the Mind in 1982. These include Gödel ‘s incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical.

Rudy Rucker: Infinity and the Mind. 1997: Rudy Rucker: Infinity and the Mind (paperback e. A table of contents is missing for this source work. php?title Book:Rudy Rucker/Infinity and the Mind&oldid 329368". Categories: Contents Wanted.

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In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.

Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Hallolan
As a university professor I read zillions of, frankly often quite dreadful, mathematics and physics and astronomy books. I read this one when it first came out in 1982. It really bowled [or Booled?] me over even then, and every time I've picked it up since I find something new and clever I hadn't given full thought to before. It is a MUCH better introduction to transfinite numbers than the also still quite good book by the late David Wallace Foster [if I've ordered names those correctly]. When I say it's one of the five best science books ever written, I am not exaggerating, provided, of course, that you have a basic grasp of Calculus and a touch of "naive set theory" and basic analysis under your belt, which if you got through high school or college you probably do. Rucker's non-fiction books are always excellent. His fiction doesn't interest me as much, but some of the stories have interesting conceptual leaps etc.
Now what are the four OTHER TOP FIVE SCIENCE BOOKS? Well, George Gamow's "Mr. Tompkins" books are pretty darn good but a bit dated in presentations. Stan Ulam's auto?-biography is good as well, As are the two books on the making of the A and H bombs. It was Ulam BTW who really figured most of it out. But those are not top fiver. "A Primer of Real Functions" by Ralph Boaz is great, as is the old ? Thomas Very Complete "Calculus" book. [In fact it was so complete you couldn't really get through the work even teach a three quarter series of courses with it. [Ah, such a noble task!] I remember they used it at Macalester College when I was there in the early 70s. They were very proud of using such an advanced text too, as they should have been. Try using the same books these days, and the students would probably immediately haul you off to the Provost and try to get you fired for giving them "thinking headaches." ... but I'm not getting starting to get bitter after 30+ years of teaching ... am I? Oops, one last thing, as great as Rucker's book is, even he doesn't provide several intuitively helpful conceptual images of the deeply mysterious "measurable cardinal" first discovered by Ulam BTW. It still all "infinite intersections and unions of sets, ultra-filters etc., if he even goes that far down the road. Though he does say something mind-expanding like "they are so much larger than all the cardinals that come before them that they sort of stand to Aleph infinity as Aleph Nought does to a large finite," or something like that. And, even in the 28 years since my first read, I still haven't found anyone, online or off, who can conjure up an intuitive picture of measurable cardinal for me ... oh why, oh why, do I bother to go on? "Man by nature seeks to know" is all Aristotle would say.
Gunos
I won't comment on the content of the book, but I would like to comment on the Kindle edition that I bought. Some figures are hard to read, and there are several typographical errors, such as mathematical symbols missing (for example the expression (s=t & t=r) -> s=r on page 272, is just (s=t & t=r) s=r in the Kindle edition. One place, a 1 is replaced by ], and one place the lemniscate - quite an important symbol in a book on inifinity - is replaced to separate circles (the ones used for degrees). These were even split across lines. Some = have been converted to :. It seems as the kindle edition is made from scanning and OCRing the print edition, without proofreading. The errors are not so numerous or hard to spot that it made the book significantly harder to read, but they are an annoyance. I would recommend the print edition.

With technical books containing many formulas and figures, the kindle preview should always contain some sections with such elements.
Xurad
The book is as described.
Nilasida
Rudy Rucker, son of a cleric and mathematics whiz kid, produced this book on `Infinity and the Mind' years ago, but reading and re-reading it, I continue to get insights and the chance to wrap my mind around strange concepts.
`This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.'
This book was intended to be accessible by those without graduate-level education in mathematics (i.e., most of us) while still being of interest to those even at the highest levels of mathematical expertise.
Even if the goal of infinity is never reached, there is value in the journey. Rucker provides a short overview of the history of 'infinity' thinking; how one thinks about divinity is closely related often, and how one thinks about mathematical and cosmological to-the-point-of-absurdities comes into play here. Quite often infinite thinking becomes circular thinking: Aquinas's Aristotelian thinking demonstrates the circularity in asking if an infinitely powerful God can make an infinitely powerful thing; can he make an unmade thing? (Of course, we must ask the grammatical and logical questions here--does this even make sense?)
Rucker explores physical infinities, spatial infinities, numerical infinities, and more. There are infinites of the large (the universe, and beyond?), infinities of the small (what is the smallest number you can think of, then take half, then take half, then take half...), infinities that are nonetheless limited (the number of divisions of a single glass of water can be infinite, yet never exceed the volume of water in the glass), and finally the Absolute.
`In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.'
At the end of each chapter, Rucker provides puzzles and paradoxes to tantalise and confuse.
* Consider a very durable ceiling lamp that has an on-off pull string. Say the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?
Rucker explores the philosophical points of infinity with wit and care. He explores the ideas behind and implications of Gödel's Incompleteness Theorem, and leads discussion and excursion into self-referential problems and set theory problems and solutions.
He also discusses, contrary to conventional wisdom, the non-mechanisability of mathematics. We tend to think in our day that mathematics is the one mechanical-prone discipline, unlike poetry or creative arts and more 'human' endeavours. But Rucker discusses the problems of situations which require decision-making and discernment in mathematical choices that no machine can (yet!) make.
* Consider the sentence S: This sentence can never be proved. Show that if S is meaningful, then S is not provable, and that therefore you can see that S must be true. But this constitutes a proof of S. How can the paradox be resolved?
This is a beautifully complex and intriguing book on the edges of mathematics and philosophical thinking, which is nonetheless accessible and intellectually inviting. You'll wonder why math class was never this fun!